The young man was caught near Hidies Bar after police officers – who were conducting a routine check of clubs - thought he was acting in an agitated way.
A search uncovered the weapon – a carving knife – and the man was arrested.
He has appeared before the court where he pleaded guilty to carrying an offensive weapon and was sentenced to 12 months’ probation.
The Cook Islands Police Service said it has been concerned for some time about the carrying of weapons in public.
A spokesman said: “This type of incident is a demonstration of why the police need to be adequately resourced.”
The law defines offensive weapons and puts them into the context of surroundings, actions and behaviour of the person.
The spokesman added: “The night-time carrying of any such item in the vicinity of where people are gathering is a serious concern.”
Other criminal incidents over the Queen’s Birthday weekend included someone trying to set fire to a building, two cases of domestic violence, five excessive noise complaints and a motorbike crash.
There were no reports of burglaries.
Police said a young male was arrested over the weekend for attempting to set fire to a government building in Avarua. He will be appearing in Cook Islands High Court later this week. Alcohol was a contributing factor in this matter, they said.
Police asked people to keep their neighbours in mind when they were going to have a party.
They had to attend five incidents in Arorangi, Nikao, Tupapa, Muri and Vaimaanga where gatherings had got too loud. Officers issued warnings to those involved.
Alcohol has been blamed on two cases of domestic violence – one in Akaoa, the other in Inave Arorangi.
And in Kavera, police were called out to deal with a crash where a motorcyclist collided with a dog. The rider suffered head and facial injuries and was admitted to hospital.
Police are investigating the incident.